2.2. Application of Inductive Coupling Principle in LWD

Originally, a low-frequency excitation voltage is directly applied to the electrode system in LWD. However, the manufacturing process of electrodes is difficult and the electrodes are easy to wear while drilling, limiting the application of the direct excitation method. In 1967, researcher ARPS, J.J. applied the inductive coupling principle to LWD [29]. The basic principle of the inductive coupling principle is shown in Figure 4. Take the transformer as an example. As can be seen from Figure 4, the transformer is composed of a primary coil, a secondary coil and a core. The number of turns of the primary coil is N₁ and the number of turns of the secondary coil is N₂.

Basic principle of the inductive coupling principle.

By applying an AC voltage U₁ to the primary coil, an induced voltage U₂ will be generated in the secondary coil. The induced voltage U₂ is determined by the following equation:

Based on the inductive coupling principle, a stable induced voltage can be generated in the secondary coil of the transformer, which can be used as the excitation voltage of the logging instrument. The diagram of the application of the inductive coupling principle in LWD is shown in Figure 5. An excitation coil is introduced as the primary coil. The measurement path consisted of the drill collar, the pick-up electrodes, the OBM and the formation is regarded as the secondary coil. By applying an AC voltage to the excitation coil, an induced voltage u is generated at the upper and lower drill collar to provide an indirect excitation voltage for the logging instrument. Z is the impedance of the OBM and the formation.

Diagram of the application of the inductive coupling principle in LWD.

The measurement path including the drill collar, the OBM and the formation can be regarded as the secondary side of a transformer with one turn. The induced voltage u is determined by the following equation:

where u_i is the voltage of the AC source, N_t is the number of turns of the excitation coil.